英和和英

名詞

invertible matrix (複数形 invertible matrices)

1. (linear algebra) An n×n square matrix for which a corresponding inverse matrix exists, such that when they are multiplied by each other (in either order), the result is the n×n identity matrix.
   • 1975 [Prentice-Hall], Kenneth Hoffman, Analysis in Euclidean Space, Dover, 2007, page 65,

     It says that, if A is a singular matrix, then every neighborhood of A contains an invertible matrix. In other words, if A is singular, we can perturb A just a little and obtain an invertible matrix.

   • 1997, Bernard L. Johnston, Fred Richman, Numbers and Symmetry: An Introduction to Algebra, CRC Press, page 199,

     There are certain very simple invertible matrices, and every invertible matrix over a field can be built up out of them.

   • 2013, Mahya Ghandehari, Aizhan Syzdykova, Keith F. Taylor, A four dimensional continuous wavelet transform, Azita Mayeli (editor), Commutative and Noncommutative Harmonic Analysis and Applications, American Mathematical Society, page 123,

     The space of real square matrices of fixed size is a vector space whose dimension is a perfect square and the invertible matrices constitute a dense open subset of this vector space.